CAREER: Fostering "Mathematical Practices" In Urban Classrooms: Focus On Representation And Justification

Cuny City College, New York NY

Investigators

Abstract

The learning of mathematical practices, that is, the specific processes that successful mathematics learners engage in when doing mathematics, such as the use of justifications and various representations, is as important in achieving high performance in mathematics as it is to know the theory of mathematics. Yet, the role of these practices in school mathematics has been peripheral at best. Many students' experience with mathematics is limited to the memorization and practice of facts and procedures and little emphasis is placed on the development of these practices. This is particularly true in diverse, urban environments where students have been traditionally under-performing in mathematics. However, recent reform efforts are calling for a shift of mathematics instruction to foster the development of such practices in all students. If these practices are to become a meaningful part of school mathematics programs, we must advance our understanding of students' development of these practices and the conditions that promote that development. While research has provided us with valuable insights on several of these practices, there has been little understanding of how these practices develop as a whole and over time especially in challenging instructional settings. I am proposing a study that will address this topic. This study will trace the development of middle school students' competencies in the mathematical practices of representation and justification and will identify conditions that influence that development. I will begin first with a broad analysis of a large number of urban students' conceptions of mathematical practices. This will be followed by a focused and detailed analysis of the development of 6th to 8th grade students, using a variety of instruments and classroom observations. The goal is to go beyond documentation of the current conditions, and to trace and understand changes in students' competencies over time. Furthermore, the study will analyze classroom-teaching practices that influence these changes. To achieve this, the students' teachers will participate in concurrent professional development activities designed to enhance their understandings of middle school students' development of mathematical reasoning and classroom practices that promote that development, and will also be studied in parallel with their students. Intellectual Merit. The proposed work addresses calls for new research programs in emerging areas, including those that attend to the development of mathematical practices. The study will lead to conceptual frameworks that coordinate social and cognitive perspectives on mathematics learning with much-needed work in the urban schools' context and in the area of middle school students' development of mathematical practices (and not only skills and facts) and how to engage in professional development for teachers that supports this. The result will be deeper insight into the forms of pedagogy and content that support student learning in urban mathematics programs. Broader Impacts. I expect the proposed work to open new avenues in the learning and teaching of middle school mathematics, in particular, in the teaching and learning of mathematical practices, in ways, which resonate with overall progressive trends in the mathematics education community. A better understanding of the processes associated with students' developing conceptions of these practices can lead to recommendations for curriculum development and instruction. This study will suggest how instruction on representation and justification might be more effectively incorporated in middle school mathematics and will provide some insights on the nature of the cognitive and social obstacles that inhibit the development of efficient mathematical reasoning in more advanced levels. The proposed research setting is situated in a major urban area with a diverse student population for whom traditional mathematics instruction has not proven fruitful. Thus, understanding how to build mathematically successful students and how to support teachers within this context can support learning across multiple and diverse student populations. Findings will be broadly disseminated to enhance the field's understanding and to assist teachers in their everyday activities. Overall, the activities of the project will directly impact the diverse urban community of New York and will mentor pre-service teachers and graduate students who are members of underrepresented groups. Finbarr C. Sloane Ph.D. Program Director REC: ROLE & IERI